In flight, the application of moderate down elevator unexpectedly causes the aircraft to dive steeply and can even continue until inverted.

Cause: CG too far aft. Negative Static Margin. 

Fix: Move CG forward.

Comment: If CG is too far aft then Static Margin can become negative. The aeroplane will have negative instability. "Tucking In" is one manifest of this.

Related Articles: 

Neutral Point and Static Margin. 1. Visualisation.

Neutral Point and Static Margin. 2. The Winning Formula.

Neutral Point and Static Margin. 3. Software.

Neutral Point and Static Margin 4. Tucking In

Neutral Point and Static Margin. 5. Stall On Landing Approach

Neutral Point and Static Margin. 6. Aircraft unstable about the Pitch, or lateral Axis.